Coarse-grained molecular dynamics study of block copolymer/nanoparticle composites under elongational flow

Simultaneous uniaxial extensional deformation and cylindrical confinement of block copolymers using non-equilibrium molecular dynamics

Using coarse-grained nonequilibrium molecular dynamics, symmetric block copolymers are simulated under the combined effects of cylindrical confinement and uniaxial extensional deformation. For a given confinement diameter, a block copolymer (BCP) will self-assemble into a fixed number of concentric cylinder lamellae at equilibrium. The changing diameter during uniaxial extensional deformation therefore is expected to affect the morphology of the BCPs. The aim of this study is to investigate the interplay of deformation and confinement on BCP morphology by varying the simulation strain rate and diameter. Two different simulation approaches are conducted: constant time simulations with varying initial diameter and constant strain simulations with varying simulation time. A comparison of self-assembly at different strain rates shows that for low strain rates, near-equilibrium morphology can form despite the deformation, while for progressively higher strain rates, extra lamellae and disordered morphologies appear. By defining a Weissenberg number based on the deformation and polymer self-assembly time-scales, the morphologies at different strain rates and diameters are explained. Using the time scale analysis, ordered morphologies appear for Wi < 1, while extra lamellae and disordered morphologies occur at Wi > 1. For the latter case, the cylinder diameter shrinks too quickly for polymers to form the equilibrium morphology, which results in a mixture of lamellar structures along the cylinder length.

Designing an ordered template of cylindrical arrays based on a simple flat plate confinement of block copolymers: a coarse-grained molecular dynamics study

In this paper we study the morphology formed by asymmetric di-block copolymers (di-BCPs) under various confinements using a large-scale coarse-grained molecular dynamics (CGMD) framework. We start with a simple flat plate confinement with the bottom and the top substrate attractive to the minor phase. Studies at a lower confinement length of 17σ have shown that there exists a critical chain length above which a transition from a three-domain morphology to a two-domain morphology is observed. Increasing the confinement length to 42σ, where the chains experience considerably lower confinement effects, also revealed the existence of a critical chain length - a transition from a multi-domain morphology (>3) to a three-domain morphology. The results obtained from the flat plate study with two confinement dimensions were used to design a topography of silica pillars with and without a bottom substrate to form ordered cylindrical BCP arrays. The least and highest radial separation lengths between adjacent pillars are kept at 17σ and 42σ, respectively. A direct correlation was observed in the number of continuous micro-domains of the maximum and minimum confinement dimensions with the 17σ and 42σ flat plate trials. With the optimum chain length employed, the surfaces with affinity to the minor phase can direct the BCP self-assembly to form ordered arrays of minor phase cylinders. The current study thus elucidates a useful tool to predict the morphology formed in an intricate nano-lithographic template by using simple length scale arguments derived from a flat plate confinement study.

Controlling the Placement of Spherical Nanoparticles in Electrically Driven Polymer Jets and its Application to Li-Ion Battery Anodes

Employing circumferentially uniform air flow through the sheath layer of the concentric coaxial nozzle, the gas-assisted electrospinning (GAES) utilizes both high electric field and controlled air flow to produce nanofibers. The ability to tailor the distribution of various nanofillers (1.85-12.92 vol% of spherical SiO₂ and Si nanoparticles) in a polyvinyl alcohol jet is demonstrated by varying airflow rates in GAES. The distribution of nanofillers is measured from transmission electron microscopy and is analyzed using an image processing technique to perform the dispersion area analysis and obtain the most probable separation between nanoparticles using fast Fourier transform (FFT). The analysis in this study indicates an additional 350% improvement in dispersion area with the application of high but controlled airflow, and a 75 percent decrease in separation between nanoparticles from the FFT. The experiments in this study are in good agreement with a coarse-grained MD simulation prediction for a polymer nanocomposite system subjected to extensional deformation. Lastly, utilizing the sheath layer air flow in production of Li-battery anode material, a 680 mAh g^-1 improvement is observed in capacity for nanofibers spun via GAES compared to ES at the same Si NP loading, which is associated with better dispersion of the electrochemically active nanoparticles.

Effect of elongational flow on immiscible polymer blend/nanoparticle composites: a molecular dynamics study

Using coarse-grained nonequilibrium molecular dynamics, the dynamics of a blend of the equal ratio of immiscible polymers mixed with nanoparticles (NP) are simulated. The simulations are conducted under planar elongational flow, which affects the dispersion of the NPs and the self-assembly morphology. The goal of this study is to investigate the effect of planar elongational flow on the nanocomposite blend system as well as to thoroughly compare the blend to an analogous symmetric block copolymer (BCP) system to understand the role of the polymer structure on the morphology and NP dispersion. Two types of spherical NPs are considered: (1) selective NPs that are attracted to one of the polymer components and (2) nonselective NPs that are neutral to both components. A comparison of the blend and BCP systems reveals that for selective NP, the blend system shows a much broader NP distribution in the selective phase than the BCP phase. This is due to a more uniform distribution of polymer chain ends throughout the selective phase in the blend system than the BCP system. For nonselective NP, the blend and BCP systems show similar results for low elongation rates, but the NP peak in the BCP system broadens as elongation rates approach the order-disorder transition. In addition, the presence of NP is found to affect the morphology transitions of both the blend and BCP systems, depending on the NP type.

Tailoring nanorod alignment in a polymer matrix by elongational flow under confinement: simulation, experiments, and surface enhanced Raman scattering application

Mesoscale simulation, electrospinning and Raman scattering experiments have been carried out to demonstrate that examination and control of nanorod configuration in a polymer matrix under elongational flow and confinement can lead to enhanced sensing. First, coarse-grained molecular dynamics (CGMD) was employed to probe the diffusivity, orientation, and dispersion of nanorods in a model polymer melt under planar elongational flow. Compared to shear flow, elongational flow gives rise to enhanced dispersion and orientation of nanorods, which are predicted to be improved with increasing the aspect ratio of nanorods and polymer chain length. As comparative experiments, we have electrospun gold (Au) nanorods with polyvinyl alcohol (PVA), and the resulting Au nanorod configuration in PVA nanofibers is in good agreement with the predicted simulation. Furthermore, coaxial electrospinning of Au nanorod/PVA-PVA (shell-core) was applied to selectively place Au nanorods in the cylindrical sheath layer, and the alignment of Au nanorods near the fiber surface was confirmed by TEM analysis and CGMD simulation under uniaxial elongation. Finally, the Au nanorod-PVA fibers were tested for surface-enhanced Raman spectroscopy for sensing applications. The coaxially electrospun fibers have demonstrated much greater signal peak strength when compared with monoaxially electrospun fibers with the same Au nanorod loading. This comprehensive study demonstrates how extensional flow and multi-layered fluids can direct the orientation and dispersion of nanorod in a polymer matrix, leading to enhanced sensing performance.

Theory and simulation studies of effective interactions, phase behavior and morphology in polymer nanocomposites

Polymer nanocomposites are a class of materials that consist of a polymer matrix filled with inorganic/organic nanoscale additives that enhance the inherent macroscopic (mechanical, optical and electronic) properties of the polymer matrix. Over the past few decades such materials have received tremendous attention from experimentalists, theoreticians, and computational scientists. These studies have revealed that the macroscopic properties of polymer nanocomposites depend strongly on the (microscopic) morphology of the constituent nanoscale additives in the polymer matrix. As a consequence, intense research efforts have been directed to understand the relationships between interactions, morphology, and the phase behavior of polymer nanocomposites. Theory and simulations have proven to be useful tools in this regard due to their ability to link molecular level features of the polymer and nanoparticle additives to the resulting morphology within the composite. In this article we review recent theory and simulation studies, presenting briefly the methodological developments underlying PRISM theories, density functional theory, self-consistent field theory approaches, and atomistic and coarse-grained molecular simulations. We first discuss the studies on polymer nanocomposites with bare or un-functionalized nanoparticles as additives, followed by a review of recent work on composites containing polymer grafted or functionalized nanoparticles as additives. We conclude each section with a brief outlook on some potential future directions.

Transient-time correlation function applied to mixed shear and elongational flows

The transient-time correlation function (TTCF) method is used to calculate the nonlinear response of a homogeneous atomic fluid close to equilibrium. The TTCF response of the pressure tensor subjected to a time-independent planar mixed flow of shear and elongation is compared to directly averaged non-equilibrium molecular dynamics (NEMD) simulations. We discuss the consequence of noise in simulations with a small rate of deformation. The generalized viscosity for planar mixed flow is also calculated with TTCF. We find that for small rates of deformation, TTCF is far more efficient than direct averages of NEMD simulations. Therefore, TTCF can be applied to fluids with deformation rates which are much smaller than those commonly used in NEMD simulations. Ultimately, TTCF applied to molecular systems is amenable to direct comparison between NEMD simulations and experiments and so in principle can be used to study the rheology of polymer melts in industrial processes.

A comparison of implicit- and explicit-solvent simulations of self-assembly in block copolymer and solute systems

We have developed explicit- and implicit-solvent models for the flash nanoprecipitation process, which involves rapid coprecipitation of block copolymers and solutes by changing solvent quality. The explicit-solvent model uses the dissipative particle dynamics (DPD) method and the implicit-solvent model uses the Brownian dynamics (BD) method. Each of the two models was parameterized to match key properties of the diblock copolymer (specifically, critical micelle concentration, diffusion coefficient, polystyrene melt density, and polyethylene glycol radius of gyration) and the hydrophobic solute (aqueous solubility, diffusion coefficient, and solid density). The models were simulated in the limit of instantaneous mixing of solvent with antisolvent. Despite the significant differences in the potentials employed in the implicit- and explicit-solvent models, the polymer-stabilized nanoparticles formed in both sets of simulations are similar in size and structure; however, the dynamic evolution of the two simulations is quite different. Nanoparticles in the BD simulations have diffusion coefficients that follow Rouse behavior (D ∝ M(-1)), whereas those in the DPD simulations have diffusion coefficients that are close to the values predicted by the Stokes-Einstein relation (D ∝ R(-1)). As the nanoparticles become larger, the discrepancy between diffusion coefficients grows. As a consequence, BD simulations produce increasingly slower aggregation dynamics with respect to real time and result in an unphysical evolution of the nanoparticle size distribution. Surface area per polymer of the stable explicit-solvent nanoparticles agrees well with experimental values, whereas the implicit-solvent nanoparticles are stable when the surface area per particle is roughly two to four times larger. We conclude that implicit-solvent models may produce questionable results when simulating nonequilibrium processes in which hydrodynamics play a critical role.